# [R] meaning of frailty estimates

Emanuela Rossi emanuela.rossi at unimib.it
Fri Oct 29 14:14:34 CEST 2004

```Sorry, but I have some difficulties to properly interpret these kind of
hazard ratios without reference group.

I'm studying the risk of introduction on a particular virus in poultry
farms. My frailty variables is the specie (1, 2, 3, 4 are four types of
poultry species which, I suppose, have different risk level, because of
different management). The other variables are other covariates related to
the farms.

QUESTION:

Which is the right interpretation of the hazard ratios relative to the
species, if we can't say they are the increase in term of hazard with
respect to another category?

Thanks

Emanuela

> > Here the output. "Specie" is the frailty variable, with four types of
>
> They are hazard ratios. There is no reference group, instead the log
> hazard ratios sum to zero (hazard ratios multiply to 1).
>
>   -thomas
>
>
> --------------------------------------------------------------------------
--
> > ------------------------------
> >
> >>
> >
> > ")
> >> fit_13_2_sp<-coxph(Surv(DATA_INI1,DATA_FIN1,EVENT1)~
V1+V2+Z+G+dim+frailty.gaussian(specie)+cluster(ID),data=SURV1)
> >> summary(fit_13_2_sp)
> > Call:
> > coxph(formula = Surv(DATA_INI1, DATA_FIN1, EVENT1) ~ V1 + V2 + Z + G +
dim + frailty.gaussian(specie) + cluster(ID), data = SURV1)
> >
> >  n= 233450
> >                         coef       se(coef)   se2             Chisq  DF
> > p
> > V1                  0.04995   0.14021  0.145916    0.13  1.00  7.2e-01
> > V2                 -0.79656   0.20483  0.197135  15.12 1.00  1.0e-04
> > Z                    -0.00359  0.00067  0.000841   28.76 1.00  8.2e-08
> > G                     0.08186  0.00583  0.005796 196.91 1.00  0.0e+00
> > dim                  0.39410  0.06981  0.057294   31.87 1.00  1.6e-08
> > frailty.gaussian(specie)                                    181.44 2.95
> > 0.0e+00
> >
> >        exp(coef) exp(-coef) lower .95 upper .95
> > V1          0.951      1.051     0.723     1.252
> > V2          0.451      2.218     0.302     0.674
> > Z           0.996      1.004     0.995     0.998
> > G           1.085      0.921     1.073     1.098
> > dim         1.483      0.674     1.293     1.700
> > gauss:1     2.504      0.399     2.108     2.975
> > gauss:2     1.799      0.556     1.457     2.221
> > gauss:3     0.278      3.599     0.217     0.356
> > gauss:4     0.799      1.252     0.641     0.996
> >
> > Iterations: 5 outer, 11 Newton-Raphson
> >     Variance of random effect= 0.975
> > Degrees of freedom for terms= 1 1 1 1 1 3
> > Rsquare= 0.003   (max possible= 0.025 )
> > Likelihood ratio test= 810  on 7.95 df,   p=0
> > Wald test            = 600  on 7.95 df,   p=0,   Robust = 355  p=0
> >
>
> --------------------------------------------------------------------------
--
> > -------------------------------------------
> >
> >
> > Thanks
> >
> > Emanuela
> >
> >
> >>> Hello,
> >>>
> >>> I'm trying to estimate a Cox's survival model with a random effect, so
I
> >>> have added the instruction frailty.gaussian (name variable) in the
> >>> model.
> >>>
> >>> My frailty variable is a qualitative variable with four types of
> >>>
> >>> In the resulting output there are the parameter estimates of all the
> >>> variables, but there are also four estimates for each type of answer
of
> >>> the frailty variable. Which kind of estimates are they? Maybe hazard
> >>> ratio? But which is the reference?
> >>>
> >>
> >> Perhaps you could post this output so we know what you are talking
> >>
> >>   -thomas
> >>
> >
> >
>
> Thomas Lumley Assoc. Professor, Biostatistics
> tlumley at u.washington.edu University of Washington, Seattle

```